ABSRACTS of PAPERS CHICAGO Abstracts of Papers Presented at MathFest 2017 Chicago, IL July 26 – 29, 2017 Published and Distributed by The Mathematical Association of America Contents Invited Addresses 1 Earle Raymond Hedrick Lecture Series by Dusa McDuff . 1 What is Symplectic Geometry? An Introduction to Some Concepts and Open Questions Lecture 1: Thursday, July 27, 10:30–11:20 AM, International Ballroom North Lecture 2: Friday, July 28, 9:30–10:20 AM, International Ballroom North Lecture 3: Saturday, July 29, 9:30–10:20 AM, International Ballroom North . 1 AMS-MAA Joint Invited Address . 1 Computational Math Meets Geometry by Douglas Arnold Thursday, July 27, 9:30–10:20 AM, International Ballroom North . 1 MAA Invited Addresses . 1 An Introduction to Spatial Graph Theory by Erica Flapan Thursday, July 27, 8:30–9:20 AM, International Ballroom North . 1 Is There a Better Way to Elect a President? by Steven Brams Friday, July 28, 10:30–11:20 AM, International Ballroom North . 2 How to Create Periodic Functions from Geometric Shapes by Ronald Mickens Saturday, July 29, 10:30–11:20 AM, International Ballroom North . 2 MAA James R.C. Leitzel Lecture . 2 Math’s Other Half by Dan Meyer Saturday, July 29, 8:30–9:20 AM, International Ballroom North . 2 AWM-MAA Etta Z. Falconer Lecture . 2 Not So Hidden Figures: Unveiling Mathematical Talent by Talithia Williams Friday, July 28, 8:30–9:20 AM, International Ballroom North . 2 MAA Chan Stanek Lecture for Students . 3 Four Tales of Impossibility by David Richeson Thursday, July 27, 1:00–1:50 PM, International Ballroom South . 3 Pi Mu Epsilon J. Sutherland Frame Lecture . 3 Bones and Teeth: Analyzing Shapes for Evolutionary Biology by Ingrid Daubechies Wednesday, July 26, 8:00–8:50 PM, International Ballroom North . 3 NAM David Harold Blackwell Lecture . 3 Hidden Figures: My Role as a Math Consultant for this Film by Rudy L. Horne Friday, July 28, 1:00–1:50 PM, International Ballroom South . 3 Alder Awards 4 Alder Award Session Friday, July 28, 2:30–3:20 PM, International Ballroom North . 4 Tell Me How You Got Here by Steven Klee Friday, July 28, 2:30–2:50 PM, International Ballroom North . 4 Teaching Mathematics as Though Their Lives Depend on It by Mary De Raeve Beisiegel Friday, July 28, 3:00–3:20 PM, International Ballroom North . 4 Invited Paper Sessions 5 Spatial Graph Theory Thursday, July 27, 1:00–5:00 PM, Continental Ballroom A . 5 Big Ideas About Big (and Less Than Big) Data Thursday, July 27, 2:00–5:500 PM, Continental Ballroom B . 6 iii iv Contents Low Dimensional Symplectic and Contact Topology Friday, July 28, 1:00–4:00 PM, Continental Ballroom B . 8 Mathematics and Democracy Friday, July 28, 2:00–5:00 PM, Continental Ballroom A . 9 No Longer Hidden Figures: Women Mathematicians Share Their Path to the Profession Friday, July 28, 2:00–5:00 PM, Salon A-3 . 10 The Life and Legacy of J Ernest Wilkins (1923-2011) Saturday, July 29, 1:00–4:00 PM, Salon A-3 . 11 Contributed Paper Sessions with Themes 13 My Favorite Math Circle Problem Part A: Thursday, July 27, 1:00–3:15 PM, Salon C-1 & C-2 . 13 Part B: Friday, July 28, 1:00–3:55 PM, Salon C-1 & C-2 . 14 Innovative Approaches to Calculus Preparation Part A: Thursday, July 27, 1:00–3:55 PM, Salon A-3 . 15 Part B: Friday, July 28, 8:30–11:05 AM, Salon A-3 . 17 Enrichment, Experiences, and Examples with Modeling in Differential Equations Courses Thursday, July 27, 1:00–4:15 PM, Salon A-4 . 19 Encouraging Effective Teaching Innovation Part A: Thursday, July 27, 1:00–4:55 PM, Salon C-4 . 21 Part B: Friday, July 28, 8:30–11:45 AM, Salon C-4 . 24 Recreational Mathematics: Puzzles, Card Tricks, Games, Gambling and Sports Part A: Thursday, July 27, 2:00–4:35 PM, Salon A-1 . 26 Part B: Friday, July 28, 2:00–4:55 PM, Salon A-1 . 28 Novel Introductions to Number Theory Thursday, July 27, 3:00–4:35 PM, Salon C-6 . 29 Inquiry-Based Teaching and Learning Part A: Friday, July 28, 8:30–11:05 AM, Salon A-2 . 30 Part B: Saturday, July 29, 8:30–11:45 AM, Salon A-2 . 32 Part C: Saturday, July 29, 1:00–3:15 PM, Salon A-2 . 34 Data Science: Big Data, Big Questions Friday, July 28, 8:30 AM–12:05 PM, Salon A-1 . 35 Writing Across the Curriculum in Mathematics Part A: Friday, July 28, 11:10–11:45 AM, Salon A-2 . 37 Part B: Friday, July 28, 1:00–4:55 PM, Salon A-2 . 38 Math Potluck: A Student Swap Session Saturday, July 29, 1:00–2:55 PM, Salon A-4 . 40 Undergraduate Research Activities in Mathematical and Computational Biology Friday, July 28, 1:00–3:35 PM, Salon A-4 . 42 Connecting Introductory Mathematics Courses to Students’ Intended Majors and Careers Friday, July 28, 1:00–4:55 PM, Salon C-4 . 43 Exploring Zeros of Polynomials Friday, July 28, 1:00–5:35 PM, Salon C-6 . 46 Mathematics in Video Games Saturday, July 29, 9:30–10:35 AM, Salon A-5 . 49 Online Assessment: Where We Have Been, Where We Are and Where We Are Going Saturday, July 29, 1:00–3:35 PM, Salon C-6 . 49 Euclid and the Mathematics of Antiquity in the 21st Century Saturday, July 29, 1:00–4:15 PM, Salon A-1 . 51 General Contributed Paper Sessions 54 Analysis Thursday, July 27, 8:30–9:40 AM, Salon C-6 . 54 History and the Philosophy of Mathematics Thursday, July 27, 8:30–9:40 AM, Salon C-8 . 55 Contents v Algebra Thursday, July 27, 8:30–10:10 AM, Salon C-7 . 56 Geometry Thursday, July 27, 1:00–3:25 PM, Salon A-2 . 57 Applied Mathematics Thursday, July 27, 1:00–3:55 PM, Salon C-7 . 58 Outreach, Mentoring and Assessment Thursday, July 27, 1:00–4:40 PM, Salon C-8 . 61 Number Theory Friday, July 28, 8:30–10:40 AM, Salon C-8 . 63 Teaching and Learning Advanced Mathematics Friday, July 28, 8:30–11:40 AM, Salon C-7 . 65 Teaching and Learning Calculus, and Mathematics and Technology Friday, July 28, 1:00–3:40 PM, Salon C-8 . 67 Modeling or Applications Friday, July 28, 1:00–4:40 PM, Salon C-7 . 69 Teaching and Learning Developmental Mathematics Saturday, July 29, 8:30–9:55 AM, Salon C-6 . 71 Probability and Statistics Saturday, July 29, 8:30–10:40 AM, Salon C-7 . 73 Graph Theory Saturday, July 29, 1:00–3:10 PM, Salon C-8 . 74 Teaching and Learning Introductory Mathematics Saturday, July 29, 1:00–4:10 PM, Salon C-7 . 75 Graduate Student Session 78 Great Talks for a General Audience: Coached Presentations by Graduate Students Saturday, July 29, 1:00–5:00 PM, Boulevard A . 78 Saturday, July 29, 1:00–5:00 PM, Boulevard B . 79 PosterFest 2017 80 PosterFest 2017 Friday, July 28, 3:30–5:00 PM, Salon D . 80 Index of Speakers 83 Invited Addresses 1 Invited Addresses Earle Raymond Hedrick Lecture Series Dusa McDuff Barnard College, Columbia University What is Symplectic Geometry? An Introduction to Some Concepts and Open Questions Lecture 1: Thursday, July 27, 10:30–11:20 AM, International Ballroom North Lecture 2: Friday, July 28, 9:30–10:20 AM, International Ballroom North Lecture 3: Saturday, July 29, 9:30–10:20 AM, International Ballroom North Symplectic geometry has many faces. It takes place in even dimensions, and can be considered a version of complex algebraic geometry that is not constrained by the requirement that functions be polynomial, or more generally complex analytic. It also gives a framework in which to describe energy-conserving flows, and so has many applications to questions in dynamics. Recently it has turned out that symplectic structures (and their odd dimensional analog contact structures) can be used to help understand purely topological questions such as the possible ways that a circle can be twisted up in three-dimensional space, i.e. knot theory. This set of lectures will first describe what a symplectic structure is, and then explain why such structures are interesting. Most of our examples will be very concrete and will concern objects in two, three and four dimensions. We will assume knowledge of multivariable calculus and basic linear algebra, but not too much else. AMS-MAA Joint Invited Address Thursday, July 27, 9:30–10:20 AM, International Ballroom North Douglas Arnold University of Minnesota Computational Math Meets Geometry One of the joys of mathematical research occurs when seemingly distant branches of math come together. A beautiful example occurred over the last decade with the development of the field of compatible, or structure-preserving, discretizations of differential equations, in which ideas from topology and geometry have come to play a key role in numerical analysis. Very roughly, instead of applying standard all-purpose algorithms, such as Runge-Kutta methods and linear multistep methods for ODEs and finite difference or finite element methods for PDEs, far better results can be obtained for various classes of problems by constructing discretization methods which exactly preserve key geometric structures underlying the equations under consideration. Such structures include, for ordinary differential equations, symplecticity, symmetry, invariants and constraints, and, for partial differential equations, de Rham and other cohomologies and associated Hodge theory.